Transient transmission of THz metamaterial antennas by ...metamaterials.riken.jp/tanaka/AccomplishmentFiles/Opt...Research Article Vol. 29, No. 1/4 January 2021/Optics Express 170

Research Article Vol. 29, No. 1 / 4 January 2021 / Optics Express 170

Transient transmission of THz metamaterialantennas by impact ionization in a siliconsubstrateMATIAS BEJIDE,1 YEJUN LI,1,2 NIKOLAS STAVRIAS,3 BRITTAREDLICH,3 TAKUO TANAKA,4,5 VU DINH LAM,6 NGUYEN THANHTUNG,6,7 AND EWALD JANSSENS1,81Quantum Solid-State Physics, Department of Physics and Astronomy, KU Leuven, Leuven, Belgium2Department of Physics and Electronics, Central South University, Changsha, China3FELIX Laboratory, Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands4Metamaterials Laboratory, RIKEN Cluster for Pioneering Research, Saitama, Japan5Innovative Photon Manipulation Research Team, RIKEN Center for Advanced Photonics, Saitama, Japan6Institute of Materials Science and Graduate University of Science and Technology, Vietnam Academy ofScience and Technology, [email protected]@kuleuven.be

Abstract: The picosecond dynamics of excited charge carriers in the silicon substrate of THzmetamaterial antennas was studied at different wavelengths. Time-resolved THz pump-THzprobe spectroscopy was performed with light from a tunable free electron laser in the 9.3–16.7THz frequency range using fluences of 2–12 J/m2. Depending on the excitation wavelengthwith respect to the resonance center, transient transmission increase, decrease, or a combinationof both was observed. The transient transmission changes can be explained by local electricfield enhancement, which induces impact ionization in the silicon substrate, increasing thelocal number of charge carriers by several orders of magnitude, and their subsequent diffusionand recombination. The studied metamaterials can be integrated with common semiconductordevices and can potentially be used in sensing applications and THz energy harvesting.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The electromagnetic properties of metamaterials (MM) depend on the size and periodic ar-rangement of the components [1–3]. The building blocks of terahertz (THz) MMs, operatingin the 0.5–15 THz range, have typical sizes of a few to hundreds of micrometres. In this sizerange photolithography is a mature fabrication technology. By changing the size and shape ofthe components, their environment, and the proximity of the neighbouring components; theresonance frequency, bandwidth and the resonance type can be tuned [4–6]. For example, dipoleantennas interact strongly with the electric field, while split rings resonate with magnetic fields[7–9].

The THz range, with frequencies in between high frequency electronics (GHz, radio waves)and photonics (from infrared to near UV), is still relatively unexplored. The development of THzradiation sources has greatly advanced the last decades due to optical rectification and opticallypumped sources [10–12], while short high-power laser pulses with a large tunable range arestill only achievable through vacuum electronics, e.g. free electron lasers. THz frequenciesare particularly well suited for research of MMs and THz MM technology, where absorbers,detectors, and modulators have been developed in the last decades [13–15]. Bridging the THzgap may bring great advances to different areas, ranging from basic research in physics andastronomy to medical imaging, telecommunication, single electron control in nanostructures, and

#405555 https://doi.org/10.1364/OE.405555Journal © 2021 Received 17 Aug 2020; revised 4 Dec 2020; accepted 8 Dec 2020; published 22 Dec 2020

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even the construction sector [13,16]. In particular, THz MMs could be used in the field of energyharvesting since objects above 50 K radiate in the THz range and THz radiation surrounds us ingreat quantities and in the field of telecommunication because their frequencies allow for thetransmission of high-density data streams [3,14,17–20].

Many of the applications listed above are based on nonlinear effects induced by field enhance-ment (FE) in a semiconducting substrate or inter-antenna nonlinear materials. The FE resultsfrom the confinement of the incident electromagnetic fields by the MMs structures. Knowledgeabout the dynamical processes induced by the FE are important for the design and constructionof MMs with improved tunability of their ultrafast properties [3,14,17,21]. In particular, it wasshown that THz FE can induce strong charge carrier multiplication in semiconducting materialssuch as GaAs and silicon [18,19,22,23], which is relevant for photovoltaics, luminescent emitters,and photon detectors. THz spectroscopy is a powerful technique with high potential to study theeffect of FE induced nonlinearities on the optical properties of THz MMs [18,24], but has so faronly been limited to broadband excitation and short timescales (few ps only). Knowledge aboutthe FE effects in MM is important to avoid high energy electron-induced melting and damagecaused by electromigration [25].

Not only the excitation dynamics but also the subsequent carrier relaxation processes, takingplace on time scales ranging from less than a picosecond (e.g., electron-electron scattering)to several nanoseconds (bulk electron-hole recombination), are not fully understood. THzpump-THz probe transient transmission spectroscopy, carried out in a broad spectral range aroundthe resonance frequency, can be instrumental in this respect. The development of evermorepowerful and faster THz coherent sources, e.g. free electron lasers (FELs), enables the study ofthe relaxation phenomena and transient effects in nonlinear MMs in a broad spectral range withhigh temporal resolution [10]. Because of the low availability of THz sources, the potential ofTHz pump/probe spectroscopy has so far not been fully exploited.

In this work, we study cut-wire (CW) MMs consisting of micrometer sized antennas arrangedin a rectangular lattice on top of a boron doped Si substrate. The picosecond (ps) dynamic of aMM is, for the first time, probed by THz pump/THz probe spectroscopy at different wavelengthsacross the broad transmission gap of the MMs. In combination with electromagnetic simulations,those experiments provide insight in the underlying causes of the transient transmission.

2. Experimental and computational methodology

The transient transmission of the samples was investigated with THz three beam pump-probespectroscopy (TPPS). Those experiments were carried out at the Free Electron Lasers for InfraredeXperiments (FELIX) laboratory, Nijmegen, the Netherlands [26]. FELIX is continuouslytunable in the 3–100 µm spectral range, of which the 18–38 µm range was used for the currentexperiments. The output of the free electron laser consists of 8 µs long macropulses with arepetition frequency of 10 Hz. Each macropulse consists of a train of micropulses that have aduration of 5–10 ps, corresponding to a spectral width of ∼0.5% in the 18–38 µm range (themicropulses are transform limited), with a repetition frequency of 25 MHz. The experiments areperformed with a single micropulse, which has a fluence in the range of 2–12 J/m2 delivered in 8ps [26]. It was shown that a fluence of about 20 J/m2, which is above the maximal fluence usedin the current study, can generate ripples in a silicon surface [27].

The three laser pulses (pump, probe, and reference) originate from the same micropulse. Asillustrated in Fig. 1, a first beam splitter splits off 90% of the pulse energy creating the pump beam.The remaining 10% is split into two identical pulses, the probe and the reference, which areseparated in time by half of the micropulse repetition period (i.e., 20 ns). The pump-probe delay istunable from –200 to 800 ps. The reference beam is used to balance out pulse-to-pulse fluctuationsin the laser power and spatial beam profile, increasing the sensitivity of the measurements. Thethree beams are focused on the sample using a parabolic mirror with a focal length of 152 mm,


and a pinhole is used to ensure a good overlap of the three beams. The balanced bolometerconverts the relative probe to reference transmission into a voltage. The strong pump pulseexcites the CW antennas and a delayed probe pulse monitors the transmission as a function ofthe pump-probe delay time. A negative (positive) probe transmission, relative to the referencetransmission, implies that the pump beam has induced a transient decrease (increase) of thesample transmission. This approach implicitly assumes that the initial situation is recovered 20 nsafter the pump beam passed through the sample, which is confirmed by the pump-probe dynamicsat negative times (if the probe arrives prior to the pump, an unperturbed state of the sample isobserved) and by the absence of long term drifts. It is important to mention that there was nodamage seen after the experiments upon inspection of the samples with optical microscopy, evenat the highest pump fluence.

Fig. 1. Schematic view of the pump-probe setup. It shows how the three beams (pump,probe, and reference) are derived from single FELIX pulse, and arranged to reach the samplewith desired time delays between each other. BS refers to beam splitter.

The finite integration simulation technique embedded in CST Microwave Studio software wasused to compute the dipole resonance [28]. The simulations were performed using the timedomain solver for 3.5 ns, with periodic boundaries applied for the H⃗ and E⃗ directions, whilethe propagation direction k⃗ of the incident electromagnetic wave is kept perpendicular to thesample plane. The modelled silicon substrate was 200 µm thick, which is thick enough to avoidFabry-Perot interference that tampers with the calculated spectra.

3. Results

Figure 2 shows the transmittance spectrum of the sample, measured with light polarised along thelong axis of the antennas and normalised for the transmission of the bare silicon substrate. Thelinear transmittance spectrum shows a broad transmission gap from 17 to 32 µm with a minimumaround 23 µm.

For antennas with negligible neighbour interaction, their dipole resonance wavelengths, whichcan be approximated as the transmittance minima, follow the antenna resonance equation[5,29–31]:

λres = 2 · neff L (1)with L the length of the antenna and neff the effective refraction index of the cut wires’ environment.neff depends on the dielectric constant of the substrate εsub via:

neff =√εeff =

√︁(1 + εsub)/2 (2)

The resonance frequency thus depends on the dielectric properties of the silicon substrate,which change upon exposure to an intense electric field.


Fig. 2. Experimental (measured using a FTIR setup, Bruker V80) and simulated transmit-tance spectra of the CW metamaterial sample with 4×1 µm2 antennas and a 9×5 µm2 unitcell. The left inset is a schematic cross section (not drawn to scale) of the sample and theright inset is a picture of the sample. Labels I, II, and III denote regions of the spectra withdifferent transient behaviour.

Using Eqs. (1) and (2) to fit FTIR transmission data for samples with antennas sizes rangingfrom 1 to 15 µm (see Fig. S1 in the Supplement 1), a refractive index for the substratensub = 3.26± 0.09 is found, close to the reported value of 3.417 for wavelengths around 20 µm[32]. This interpretation ignores the dependence of the wavelength (and the width) of theresonance on the coupling interaction between neighbouring CW antennas, which is small forthis geometry according to the simulations. The measured static transmittance spectrum is inoutstanding agreement with the spectrum from electromagnetic simulations (red dashed line inFig. 2).

Figure 3 shows the transient probe transmission of the samples (relative to the reference) inthe range from –100 to 650/550 ps at three different wavelengths. The results of experimentsperformed at additional wavelengths are available as Supplement 1 (Fig. S2). The fast oscillationsobserved during the first ∼15 ps of recorded signal are atributed to the interference of standingwaves formed by the incoming and reflected laser pulses, optical autocorrelation, and are ignoredin the forthcoming interpretation.

On the blue and center side of the transmittance minimum (e.g. 23 µm excitation wavelength inFig. 3(a)), a transient transmission increase is observed that lasts several hundreds of picoseconds.At the far red side of the resonance center (Fig. 3(c) at 32 µm), there is a transient transmissiondecrease. In the spectral range at the red side, but closer to resonance center (Fig. 3(b) at 27.5µm), the behavior is mixed: there is an initial decrease in the transmission (first ∼50 ps) followedby a transmission increase before decaying to the original level. Those three types of transienttransmission behavior divide the spectral range in three zones, labelled as I, II, and III in Fig. 2.Also in other samples with different CW dimensions; 2.5×1, 7×1 and 9×1 µm2; exibiting antennaresonance wavelengths at 17, 35 and 44.5 µm, respectively, similar behavior was observed (seeSupplement 1 Fig. S3, S4 and S5).

The observed wavelength dependence in the transmission change can be explained in thefollowing way. The pump pulse induces changes in the system that are reflected in a transientchange of the wavelength and intensity of the antenna resonance. As will be explained in moredetail in the discussion section, neither a red shift nor a change in the spectral width alone issufficient to explain the observed dynamics, but a combination of both effects is. It is importantto stress that pump and probe laser pulses always have the same wavelength, since they comefrom the same laser pulse. This means that for each probed wavelength, the pump was different.While the exact wavelength of the pump is not changing the nature of the phenomena taking place

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Fig. 3. Transient transmission change following excitation at (a) 23 µm with a 8 J/m2 fluence,(b) 27.5 µm with a 11 J/m2 fluence and (c) 32 µm with a 8 J/m2 fluence. The inset in panelc) presents a TPSS measurement for a bare silicon substrate (32 µm with 5 J/m2 fluence)without gold antennas. This reference measurement does not show transient transmissiondynamics asides from a signal in the first 15 ps that is caused by optical autocorrelation ofthe probe pulse.

(i.e. impact ionization, explained in the discussion section), the FE changes with the excitationwavelength. The wavelength dependence is related to proximity of the excitation wavelength tothe resonance center. To have comparable excitation conditions at different excitation wavelengths,the laser pulse energy was adjusted. Within the used range, the sample response increasesmonotonically with the laser fluence (see Supplement 1 Fig. S6), allowing for rescaling themeasured signal.

4. Discussion

For wavelengths within the broad transmission gap of the MM, the electromagnetic field of thepump pulse causes oscillation of the free electrons of the antenna, which enhances the impingingelectric field. This enhanced electric field penetrates the Si substrate and may, if it is strongenough, induce an amplification of the conduction band charge carriers. Such an increase of thecharge carriers in silicon, changes its optical and electrical properties (i.e. refractive index andconductivity) and thereby the antenna resonance wavelength and width (see Eqs. (1) and (2)).The change of the optical properties of the system can be detected as a transient transmission.

The FE factor was simulated and used to calculate the value of the penetrating E-field.Considering a 2–12 J/m2 pump pulse fluence, 0.2 mm2 spot area, and 8 ps pulse length, the value

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of the incident electric field is of the order of 0.3–0.7 MV/cm. The penetrating enhanced fieldinside the silicon substrate is in this case of the order of MV/cm.

As illustrated in Fig. 4(a), the FE of a single antenna (with a resonance wavelength of 23µm) depends on the position in the sample and on the excitation wavelength. As is expectedfor a dipolar resonance, the FE is higher close to the antenna’s edges along the short axis; inparticular, close to the corners. The maximum FE is red shifted with respect to the centerof the transmittance minimum (vertical dotted line in Fig. 4(a)). This is a well-documentedphenomenon. It is analogous to a damped forced harmonic oscillator [33], where the frequencycorresponding to the maximal energy dissipation can be related to the minimal transmittance.The frequency corresponding to the maximum oscillation amplitude is lower (red shifted) andcan be is related to the maximal FE.

Fig. 4. a) Wavelength dependence of the FE factor at different positions (labelled 1-5). Thevertical dashed line indicates the centre of the transmission gap. b) Spatial distribution ofthe enhanced electric field, the red arrows represent the direction and the magnitude of theelectric field in the area where the field is larger than the incident field. The Si substrate,located below the gold antenna, is not shown for clarity.

The enhanced electric field accelerates Si conduction band charge carriers. They may acquiresufficient energy to excite, in a scattering event, a bound valence band charge carrier to theconduction band. This mechanism for carrier multiplication is called impact ionization. Itoriginates from Coulomb interaction between energetic carriers in the conduction and valenceband of a semiconductor. [22,23] A cascade of collision events, in which free charge carriers areaccelerated by a strong external electric field, increases the number of free carriers by severalorders of magnitude. Since the conductivity directly depends on the number of charge carriers inthe conduction band, as given by the Drude model [18,22], the increased number of free carrierschanges on the electrical and optical response of the semiconductor [18,22,23,34].

The process can be represented by the following equation [23]:

e1 → e1 + e2 + h2, (3)

with e1 the conduction band electron being accelerated by the enhanced electric field, and e2 andh2 the excited valence band electron and its respective hole. The rate equation for charge carrier


amplification by impact ionization, ignoring relaxation processes, is:

dn(t)/dt = n(t) ∫ f (E, t)Yii(E)dE, (4)

with n0 the initial number of charge carriers, f (E, t) the electron energy distribution, and Yii(E) theimpact ionization rate. Based on the theory developed by Keldysh, with a quadratic dependenceof the rate on the energy of the conduction electrons [35], Cartier et al. proposed the followingexpression for the impact ionization rate [36]:

Yii(E) =∑︂3

i=1p(i)

(︄E − Eith

Eith

)︄2θ(E(t) − Eith), (5)

where the sum runs over the possible excitation pathways, namely i= 1 the indirect band gap forelectrons; i= 2 the indirect band gap for holes; and i= 3 the direct band gap for electrons. Theparameters p(i) are constants, evaluated 3.25·1010, 3.0·1012, and 6.8·1014 s−1 for i= 1, 2, and 3,respectively [36]. E(t) is the carriers’ energy, Eith corresponds to different threshold energiesfor ionization (1.2, 1.85, and 3.45 eV for i= 1, 2, 3, respectively) [36], and θ(x) is the Heavisidefunction. Given that each enhanced THz semi cycle is equivalent to a very fast electric field pulse,the electron energy distribution can be approximated as a delta function: f (E, t) = δ(E − E(t))[37]. This simplifies Eq. (4) to:

dn(t)/dt = n(t)∑︂3

i=1p(i)

(︄E(t) − Eith

Eith

)︄2θ(E(t) − Eith) (6)

To complete the model, the external electric field should be linked to the carriers’ energy. Thisis done by the momentum equation of a Bloch wave in a periodical Coulomb potential includinga term for momentum relaxation and the electron dispersion relation [23,38,39].

ℏdk(t)

dt= e ε(t) −

∑︂3i=1

k(i)th p(i)

(︄k(t) − kith

kith

)︄2θ(k(t) − kith) −

k(t)τ

. (7)

In this equation ε(t) represents the enhanced THz pulse, k(t) the carriers’ momentum, andτ the momentum decay time. The THz micro pulse is modelled as a sinusoidal wave whoseamplitude is modulated by a Gaussian envelope ε(t) = εFE cos(ω0t)exp[−1/2 · (t/σ)2], whereω0 is the angular frequency of the THz pulse and σ is related to the pulse duration. For thesimulations σ is set to 2 ps and εFE is the enhanced electric field amplitude, i.e., the incidentTHz field times the FE factor.

The momentum decay time is a complex function that depends on the carriers’ drift velocityand the intrinsic carrier-phonon scattering time. We approximate it by [40,41]:

1τ=

1τeph+

eme · µ

(8)

Here e is the electron charge, µ the electron mobility [41,42], and τeph= 240 ps the siliconelectron phonon scattering time [40]. This expression represents the energy loss of a conductionband electron due to the influence of an external electric field. This term represents the scatteringfor charge carriers in silicon.

Equations (6) to (8) describe how the Si substrate is affected by impact ionization. In Fig. 5 theresults of solving these equations for several different FE factors and wavelengths are shown. Aminimal FE of 3 seems to be needed to cause a significant increase of the number of conductionelectrons, at least one order of magnitude. It is consistent with findings in literature where for


larger bandgap semiconductors, like GaAs and Si; no transmission changes were observed unlessa threshold energy, related to a threshold electric field via Eq. (6) and the electron dispersionrelation, is surpassed [18,19,22,23]. This is achievable only through FE of the incident electricfield given the high intensity required. For narrow band semiconductors (InSb), electron impactionization could be obtained without the need for field enhancement [39]. For a given FE, longerwavelengths are more efficient to increase the charge carrier concentration due to longer opticalcycle and thus more time for the enhanced electric field to interact with the silicon substrate.

Fig. 5. Relative increase of the conduction band charge carriers as a function of the FEfactor for different excitation wavelengths. The values are calculated with a pump pulsefluence of 10 J/m2 and an initial carrier density of the Si substrate of 5·1015 /cm3.

The impact ionization model is further used together with the simulation results of the spatialand frequency dependence of the enhanced electric field, to predict the concentration of chargecarriers, and thus the conductivity of the silicon, as a function of space and time [41].

So far, the model only describes the first picoseconds when the pump pulse is exciting theantennas. The vast majority of the acquired TPPS data corresponds to later times, during whichthe enhanced carrier density decreases by electron-hole pair recombination and diffusion. Theirdensity n(t) diminishes by diffusion and recombination by trapping and neutralization. In order tomodel this, we use a characteristic decay time of τ = 200 ps to account for carrier recombination[24,43] and a density dependent ambipolar carrier diffusion coefficient D [44], to account forvolumetric expansion.

n(t) = n0exp(−t/τ)

V(t) , (9)

V(t) =√︂

6D t + v20, (10)

with n0 the carrier density after the impact ionization and V(t) the affected volume, whichincreases in time due to diffusion [18].

The measured transient signal likely results from a mixture of several types of recombinationprocesses and carrier diffusion, which affect the silicon conductivity in an expanding volumenear the antenna’s extremes [18,45].

The model provides the local change in conductivity of the substrate at every moment in timefor a given value of FE. This information is used as input for the CST simulations, considering anaverage FE value for the unit cell. Since the antenna resonance depends on the dielectric propertiesof the substrate, the transient properties of the substrate are reflected in the transmittance spectraof the samples.

The results of these simulations for an excitation wavelength of 27.5 µm and a pump pulsefluence of 11 J/m2 are shown in Fig. 6. It can be seen that the transmission gap red-shifts and


broadens during the first few ps, as expected from the results shown in Fig. 3, and thereafter, on atimescale of several tens to a few hundreds of ps, returns to the original situation.

Fig. 6. The shape of the modelled transmittance spectra at different moments afterexcitation. t= 0 ps and t= 8 ps correspond to the beginning and the end of the excitationpulse, respectively. The sample geometry corresponds to the one shown in Fig. 2 and theexcitation wavelength is 27.5 µm.

Fig. 7. Simulated transient transmission changes based on the impact ionization modeland comparison with the experimental data (same as in Fig. 3) for (a) 23 µm with a 8 J/m2fluence, (b) 27.5 µm with a 11 J/m2 fluence, and (c) 32 µm with a 8 J/m2 fluence.


Applying this approach at several wavelengths allows us to qualitatively reproduce the transienttransmission changes that were measured at different wavelengths. Figure 7 presents simulations atdifferent wavelengths and pump pulse energies, which correspond to the experimental conditionsof the TPPS traces shown in Fig. 3. Comparing the experimental and modelled transmissioncurves of Fig. 7, one finds a qualitative agreement. The simulations reproduce the observedtrends; including the different transient responses at different excitation wavelengths, and thenon-instantaneous rise to the maximum transmission change. The good agreement supports thevalidity of the proposed model for the carrier dynamics. Quantitative differences can be attributedto a rough description of momentum/energy dissipation of the excited charge carriers during theimpact ionization; oversimplification of the conductivity changes in the affected silicon volumeand the detailed FE spatial distribution; and inaccuracies of the simulations related to the sizeand shape of the affected volume.

5. Conclusion

We have studied the transient transmission of THz metamaterials with spectral resolution bythree-beam pump-probe spectroscopy using an infrared free electron laser. The strong THz fieldof the pump beam was found to be locally enhanced by the resonance mode of micrometer sizedcut-wire antennas. Impact ionization increases the carrier concentration in the silicon substrateby several orders of magnitude. The increase and decay of these high carrier densities results infast nonlinear changes in the optical properties of the MM. Following picosecond THz excitation,the transmission gap red-shifts and broadens during the first few picoseconds and the samplerelaxes to the original situation on a timescale of several tens to a few hundreds of ps. Thisbehavior is qualitatively reproduced and interpreted by the described impact ionization model.

MM on semiconducting substrates have potential to be used in energy harvesting devicesat THz frequencies if the materials are further optimized geometrically such that less intenseelectric fields are required to induce the strong charge carrier increase. Due to their sensitivityto the environment, those MM may also have potential in sensing applications. There are stillseveral unanswered fundamental questions about the excitation and relaxation processes. Infuture experiments one could explore substrates with different types and levels of doping, as wellas different sample temperatures. Future work could also involve different structural designs,which allow for even higher FE factors in order to maximize carrier multiplication.Funding. Laserlab-Europe (grant 654148 within the European Union’s Horizon 2020 research and innovationprogramme); Fonds Wetenschappelijk Onderzoek (G0E62.18N); National Foundation for Science and TechnologyDevelopment (FWO.103.2017.01).

Acknowledgment. The authors also thank the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)for the support of the FELIX Laboratory.

Disclosures. The authors declare no conflicts of interest. EJ and NTT conceived and designed the research; TT,VDL, and NTT prepared the samples; MB, YL, NS, BR, and EJ carried out TTPS and FTIR measurements; MB and YLanalysed the experimental data, MB, NTT, and EJ conducted the simulations and calculations; MB, NTT and EJ preparedthe manuscript. All authors have edited, reviewed and given approval to the final version of the manuscript.

See Supplement 1 for supporting content.

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